1 Chapter 4 The Laws of Motion

2 Force Force is associated with the change in the stat of motion of an object. Force is required to make an object move from stationay. What is the relation between the force on an object and the change in motion of that object?

3 4.1 Classes of Forces Contact forces involve physical contact between two objects Field forces act through empty space No physical contact is required

4 Magnitudes of Forces A spring can be used to calibrate the magnitude of a force

5 Forces are vectors Forces are vectors, so you must use the rules for vector addition to find the net force acting on an object

6 Fundamental Forces All particles in nature are subject to four fundamental forces Strong force Electromagnetic force Weak force Gravitational force This list is in order of decreasing strength

7 Nature of the four fundamental forces Gravitational forces between objects with masses Electromagnetic forces between electric charges Strong nuclear forces between subatomic particles Weak nuclear forces for certain radioactive decay processes

8 Nuclear Force Holds nucleons together Strongest of all fundamental forces Very short-ranged Less than m (1fm) Negligible for separations greater than this

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Atoms as Elementary Particles Atoms From the Greek for “indivisible” Were once thought to be the elementary particles Atom constituents Proton, neutron, and electron After 1932 (neutrons are found in this year) these were viewed as elementary for they are very stable All matter was made up of these particles

11 Discovery of New Particles New particles Beginning in 1945, many new particles were discovered in experiments involving high-energy collisions Characteristically unstable with short lifetimes ( from s to s) Over 300 have been cataloged and form a particle zoo A pattern was needed to understand all these new particles

12 Elementary Particles – Quarks Now, physicists recognize that most particles are made up of quarks Exceptions include photons, electrons and a few others The quark model has reduced the array of particles to a manageable few Protons and neutrons are not truly elementary, but are systems of tightly bound quarks

13 Electromagnetic Force Responsible for binding atoms and molecules together to form matter About times the strength of the nuclear force A long-range force that decreases in strength as the inverse square of the separation between interacting particles

14 Weak Force To account for the radioactive decay process such as beta decay in certain nuclei Its strength is about times that of the strong force Short-range force Scientists now believe the weak and electromagnetic forces are two manifestions of a single interaction, the electroweak force

15 Gravitational Force A familiar force that holds the planets, stars and galaxies together A long-range force It is about times the strength of the nuclear force Weakest of the four fundamental forces Its effect on elementary particles is negligible

16 Explanation of Forces Forces between particles are often described in terms of the exchange of field particles or quanta The force is mediated by the field particles Photons for the electromagnetic force Gluons for the nuclear force W +, W - and Z particles for the weak force Gravitons for the gravitational force

17 Forces and Mediating Particles

18 Force and Motions: Isaac Newton ( ) Three Newton’s laws of motion

Newton’s First Law: The Law of Inertia A moving object can be observed from a number of reference frame. Observers in different reference frames may describe the motion of the object differently. If an object does not interact with other objects, it is possible to identify a reference frame in which the object has zero acceleration Such a reference frame is also called an inertial frame of reference

20 Inertial Frames Any reference frame that moves with constant velocity relative to an inertial frame is itself an inertial frame A reference frame that moves with constant velocity relative to the distant stars is the best approximation of an inertial frame We can consider the Earth to be such an inertial frame although it has a small centripetal acceleration associated with its motion

21 Newton’s First Law – Alternative Statement In the absence of external forces, when viewed from an inertial reference frame, an object at rest remains at rest and an object in motion continues in motion with a constant velocity Newton’s First Law describes what happens in the absence of a force When no force acts on an object, the acceleration of the object is zero

Inertia and Mass The tendency of an object to resist any attempt to change its velocity is called inertia Mass is the property of an object that specifies how much resistance an object exhibits to change in its velocity

23 More About Mass An inherent property of an object Independent of the object’s surroundings Independent of the method used to measure it Mass is a scalar quantity The SI unit of mass is kg

24 Mass vs. Weight Mass and weight are two different quantities Weight is equal to the magnitude of the gravitational force exerted on the object The weight of an object will vary with location The mass of an object is the same everywhere

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Newton’s Second Law The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass Force is the cause of change in motion, as measured by the acceleration Algebraically,

27 More About Newton’s Second Law is the net force This is the vector sum of all the forces acting on the object Newton’s Second Law can be expressed in terms of components:  F x = m a x  F y = m a y  F z = m a z

28 Units of Force

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30 Fig 4.4

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Gravitational Force The gravitational force,, is the force that the earth exerts on an object This force is directed toward the center of the earth Its magnitude is called the weight of the object Weight = F g = mg

34 More About Weight Because it is dependent on g, the weight varies with location g, and therefore the weight, is less at higher altitudes We can compare the masses of two objects by measuring their weights. At a given location, the ratio of the weights of two objects equals the ratio of their masses.

35 Gravitational Mass vs. Inertial Mass In Newton’s first Law, the mass is the inertial mass and measures the resistance to a change in the object’s motion In the gravitational force F g =mg, the mass is determined by the gravitational attraction between the object and the Earth. The mass of an object obtained in this way is called the gravitational mass. Experiments show that gravitational mass and inertial mass have the same value

Newton’s Third Law If two objects interact, the force exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 on object 1 Note on notation: is the force exerted by A on B

37 Action-Reaction Examples, 1 The force exerted by object 1 on object 2 is equal in magnitude and opposite in direction to exerted by object 2 on object 1 Fig 4.5

38 Fig 4.5

39 Newton’s Third Law, Alternative Statements Forces always occur in pairs A single isolated force cannot exist The action force is equal in magnitude to the reaction force but opposite in direction One of the forces is the action force, the other is the reaction force It doesn’t matter which is considered the action and which the reaction The action and reaction forces must act on different objects and be of the same type

40 Action-Reaction Examples, 2 The action force (table on monitor) is the reaction of the force that the monitor exerts on the table Normal means perpendicular, in this case The action (Earth on monitor) force is equal in magnitude and opposite in direction to the reaction force (the monitor exerts on the Earth) Fig 4.6(a)

41 Normal force The normal force is a contact force that is perpendicular to the contact surface.

42 Free Body Diagram In a free body diagram, you want the forces acting on a particular object The normal force and the force of gravity are the forces that act on the monitor The normal force balances the gravitational force. Fig 4.6(b)

43 Fig 4.7

Applications of Newton’s Law Objects in equilibrium If the acceleration of an object is zero, the object is said to be in equilibrium Mathematically, the net force acting on the object is zero

45 Fig 4.9

46 Problem-Solving Hints Newton’s Laws Conceptualize the problem – draw a diagram Categorize the problem Equilibrium (  F = 0) or Newton’s Second Law (  F = m a) Analyze Draw free-body diagrams for each object Include only forces acting on the object

47 Equilibrium, Example 2a Example 4.2 Conceptualize the traffic light Categorize as an equilibrium problem No movement, so acceleration is zero Fig 4.10(a)

48 Equilibrium, Example 2b Analyze Need two free-body diagrams Apply equilibrium equation to the light and find Apply equilibrium equations to the knot and find and Fig 4.10(b)(c)

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53 Objects Experiencing a Net Force If an object that can be modeled as a particle experiences an acceleration, there must be a nonzero net force acting on it. Draw a free-body diagram Apply Newton’s Second Law in component form

54 Newton’s Second Law, Example 1a Forces acting on the crate: A tension, the magnitude of force The gravitational force, The normal force,, exerted by the floor Fig 4.8

55 Newton’s Second Law, Example 1b Apply Newton’s Second Law in component form: Solve for the unknown(s) If is constant, then a is constant and the kinematic equations can be used to more fully describe the motion of the crate

56 Inclined Planes Forces acting on the object: The normal force acts perpendicular to the plane The gravitational force acts straight down Choose the coordinate system with x along the incline and y perpendicular to the incline Replace the force of gravity with its components

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59 Fig 4.11

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64 Multiple Objects When two or more objects are connected or in contact, Newton’s laws may be applied to the system as a whole and/or to each individual object Whichever you use to solve the problem, the other approach can be used as a check

65 Multiple Objects, Example 1 Forces acting on the objects: Tension (same for both objects, one string) Gravitational force Each object has the same acceleration since they are connected Draw the free-body diagrams Apply Newton’s Laws Solve for the unknown(s) Fig 4.12

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70 Multiple Objects, Example 2 First treat the system as a whole: Apply Newton’s Laws to the individual blocks Solve for unknown(s) Check: |P 21 | = |P 12 | Fig 4.13

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77 Fig 4.14

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82 Exercises of Chapter 4 7, 14, 17, 25, 29, 31, 33, 46, 49, 51, 56

83 Exercise 49 What horizontal force must be applied to the cart shown in Figure on the right so that the blocks remain stationary relative to the cart? Assume that all surfaces, wheels, and pulley are frictionless. (Suggestion: Note that the force exerted by the string accelerates m 1.)